For number 1 The top of the piece of paper in the clue has the words '...mainframe...r the "access_1...om - if you wan...ve to wait a w... Which, with a bit of guesswork could be something like ' if you wan t in, you ha ve to wait a w hile. If we combine that with the possible six peice...

The answer is: It will never happen. With the square arrangement the distance between the rows is twice the radius, and with the triangular arrangement it is the square root of 3 times the radius (the height of an equilateral triangle with side length twice the radius). Since sqrt(3)...

For c: There are no balls in the jug. Each ball has a chance of being removed, and so, over an infinite amount of interactions, each ball is removed. But the chance of the ball being removed is not the same each time, so (while not the case here) there are probability distributions where there woul...

For c: There are no balls in the jug. Each ball has a chance of being removed, and so, over an infinite amount of interactions, each ball is removed. For b: The jug has infinitely many balls in it. As soon as we put the numbers 1 to 10 in, we remove number 10. When numbers 11 to 20 go in, number 20 ...

Problem 2: Depends on the passenger and the driver, I'm sure if they are trusting of each other it would only take 2 emails, one saying that the driver is ready and the other confirming it. That's the crux of the two General's Problem Using your scenario, we have three alternatives 1: Alice sen...

Suppose you have an minesweeper board unbounded in both height and width. Each cell on the board is a mine with probability p, otherwise an empty cell. What is the probability that there is an empty region which trivially separates all the mines into finite sets (using the algorithm most minesweepe...

edit: no, this doesn't work. Answer The clone right at the very back of the line has the first guess. Instead of saying what colour he thinks his hat is, he says what colour the hat of the clone directly infront of him is. He has a 50% chance of being right. When the guard comes back in to tell the ...

I'm probably missing something obvious, so I'd like to know what it is. This whole business with diagonals doesn't seem to me valid to me. I'm not convinced that there are any true diagonals on the carpet. On a plane, the shortest distance beween (0,3) and (4,0) is to go straight (with a length of 5...

You're right. Even leaving a card to beat the smaller of opponent's towers in the last turn doesn't necessarily help. An easy way to consistently beat your strategy would be the generally useless deck of 14×1+16, using the 1s to build two towers of 7 (the ones you ignore, maybe using some of the 1s...

I don't think it matters how many towers you play in. The average over all towers is 6 for both players in the end anyway, and all towers count. What matters is spending more points in a tower than necessary. If in the end, a player doesn't have a lead of more than one point in any tower, they neve...

The opponent only needs 1 point in each tower you don't compete in, so they will have lots of points to attack your towers. But so do I. After playing three 1s, I have 27 points left to defend those towers. As soon as my opponent starts to play cards into my towers as well as his, he spreads himsel...

Given that you don't have to play at least one card in all towers, I think a good strategy would be to completly ignore two towers, and put a small stake (1) in the other three. For every card that your opponent plays into one of your three towers, you try to match it. I've not thought this through ...

29: The man was under the influence of a Psiren. He was convinced they were about to get it on so he stripped. The Psiren sucked out his brain but his last act was to grab the straw from the Psiren as a warning to other fools who might fall into the same trap.

For example, the 4-crane version has a new level of 15 items (7 containers, a crane, and another 7 containers) added below the 3-crane version with the container-only level removed. For symmetry, add a new bottom level of 15 containers.

The answer seems to be no. I can't see how whether the moderator asks you once or a hundred times makes any difference. If you are allowed to plan ahead with your friend, then you can both count your responses until you reach your own number, and say Yes when you reach it. Because your friend is...

A man was flying overhead in a hot air balloon, when suddenly someone from below took a shot, which then went through the man in the balloon's basket. The man simply smiled, and continued to fly along, without filing any lawsuits or such. What is the cause of such strange behavior? The shot was act...

A young boy went to school one day. When he got to math class, he realized that he had a test that he didn't study for. Thinking about what to do, he decided to cheat. About half way through the test, the teacher was looking at the class to make sure no one was cheating. She looked over and saw tha...

A clean shaven 18-year-old son asked his parents if he could go to an overnight party. They agreed and let him go to the party. When he came home the next day, his parents were surprised to see that he had a fully grown beard. How did the son do it? The "overnight" party happened in the A...

That part seems pretty obvious once you say it, boggleinthesky: As for the $650, $50 goes to Hat, and $600 goes into buying 6 houses on the orange properties. Two of the houses go on New York, so its rent is now $220, and that's where Dog must have landed. You're right, that does make sense. I'...

@boggle: A drop of 650 is certainly possible if you're buying houses or hotels. Does Car have any monopolies at this point? (He must, if the table is correct... perhaps this will clarify earlier events.) Later, Car is at 80, and Dog buys something from him for 220, bringing Car up to 30...

I think the goal is ... I concur. [edit] Ignore the following, I was completely wrong @OP: Point of clarification though, I think there is a mistake in the table On the Car's 6th roll of the die , it goes from 720 to 70. That's a drop of 650, impossible in one roll on a regular monopoly boa...

I've worked out what the table means, but don't have the time this afternoon to sort it all out Ok, so the table is a collection of four players playing monopoly, with their money changing as they play the game. Each star represents that player's go, with money changing hands. Player pay each ot...

Is the female locker room getting remodeled by a load of men, and vice versa? I would assume the people doing the remodeling are probably a group of men, so while they are remodelling the men's locker room, nothing will change, but while they are remodeling the women's locker room, they swi...

The guru can not and will not ever leave the island. Even if she has blue eyes. Think about why not, and you might see where your logic train derails. Umm... Surely the guru will leave the island if she has blue eyes. Examining the two situations (Guru = Blue and Guru != blue) != Blue: We have the ...

You are confusing 2 different things I said - a statement and the proof of that statement. Ah yes. That makes sense. What doesn't work? Sorry, I hadn't fully understood your method. I was under the impression that you hadn't accounted for points chosen near the corners of the triangle, but you ...

I'm interested in jaap's first solution. Draw an equilateral triangle with height 1. From any 'random' point inside that triangle, drop perpendiculars to the triangle sides. The lengths of the three perpendiculars summed together makes 1. Is there a theorem that ensures this? I don't know o...

I think I've got it. You use the bogglesteinsky method, but you have a border of paper around it, and the middle bit is connected to the border at a single place. Photos soonish maybe. Something like the following ******************* *|---------------|* *|***************|* *|*------+------*|* *|***...

Cutting the paper along the lines will create a hole big enough to step through, so long as you cut thinly enough, and repeat the pattern enough times down the length of the paper *************** *------+------* *******|******* ------*|*------ *******|******* *------+------* *******|******* ------*|...

Ok, here's what I've got so far. Because all the numbers are consecutive (a fairly vaild assumption for magic square puzzles), we can very easily work out the magic number if we know the lowest number in the sequence. A standard 1-16 square has a magic number M of 34. A starting number n will add a ...